1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find the General Anti-derivative (Calculus I)

  1. Apr 29, 2012 #1
    1. The problem statement, all variables and given/known data
    given f(x) = [x^3+5sqrt(x)]/x^2, find the anti-derivative


    2. Relevant equations



    3. The attempt at a solution

    Hi I have attempted to solve this by re-writing the equation as a sum of two fractions:

    x^3/x^2 + 5sqrt(x)/x^2, simplying gives = x + 5/x^3/2

    I then apply the principle anti-differentiation rules, and I come out with:

    x^2/2 + 5x^-1/2 = x^2/2 + 10/sqrt(x) + C

    This answer is coming back in WebWork as wrong. I also checked my answer on wolframalpha, and got the same result.

    What am I doing wrong? (If anything)
     
  2. jcsd
  3. Apr 29, 2012 #2

    sharks

    User Avatar
    Gold Member

    Try re-writing it: [tex]x + \frac{5}{x^{3/2}}=x+5x^{-3/2}[/tex]Then integrate.
     
  4. Apr 29, 2012 #3
    I am not quite at intergration yet, this is the last section of my Calculus I course, Calculus II is intergration. So for now our anti-d's are pretty simple and just follow some basic rules.
     
  5. Apr 29, 2012 #4
    Ok so
    x + 5x-3/2 following the rule: x(n+1)/(n+1) gives

    x1+1 / (1+1) + 5x-3/2 + 2/2 / -(1/2) =

    x2/2 + 5x-1/2/ -(1/2 ) = -10x-1/2 or finally

    x2 / 2 + 10 / sqrt(x)

    I am still doing it wrong?
     
  6. Apr 29, 2012 #5
    ok yes I am doing it wrong, its - 10 / sqrt(x).

    Thank you very much.

    Story of my life, I always miss a sign.
     
  7. Apr 29, 2012 #6

    Mark44

    Staff: Mentor

    Integration is finding the antiderivative.

    Note that there is no such word in English as intergration.
     
  8. Apr 29, 2012 #7
    Thank you Mark for the insight. And you are right, there is no such word as intergration.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find the General Anti-derivative (Calculus I)
Loading...